Gravity

```					Chapter 4
Making Sense of the Universe Understanding
Motion, Energy, and Gravity
4.1 Describing Motion: Everyday
Life Examples
Our goals for learning:
How do we describe motion?
How is mass different from weight?
How do we describe motion?

Precise definitions to describe motion:
• Speed: Rate at which object moves

example: speed of 10 meters/second = 10 m/s

• Velocity: Speed and direction
example: 10 m/s, due east
How do we describe motion?

• Velocity: Speed and direction
example: 10 m/s, due east

• Acceleration: Any change in
velocity; either in direction,
magnitude, or both
The Acceleration of Gravity

 As objects fall, they
move faster & faster.

 They accelerate.

 Acceleration near
Earth’s surface from
gravity is 10
meters/second each
second.
The Acceleration of Gravity

 After 1 second, moving
10 m/s (about 22 mph)
 After 2 seconds, moving
20 m/s (about 44 mph)
 Higher you drop a ball,
greater its velocity will
be at impact…
 Unless other forces act!
The Acceleration of Gravity (g)

 Galileo demonstrated that g is the same for
all objects, regardless of their mass!

 Heavier objects (with more mass) must be
pulled more to accelerate at the same rate.
And Gravity indeed pulls more on heavier
objects!

 Confirmed by Apollo astronauts on the
Moon, where there is no air resistance.
Thought Question
Is there a net force for each of the following?
•   A car coming to a stop.
•   A bus speeding up.
•   An elevator moving up at constant
speed.
•   A bicycle going around a curve.
•   A moon orbiting Jupiter.
Thought Question
Is there a net force for each of the following?
•   A car coming to a stop. Yes
•   A bus speeding up. Yes
•   An elevator moving up at constant
speed. No
•   A bicycle going around a curve. Yes
•   A moon orbiting Jupiter. Yes
How is mass different from weight?

Mass—the amount of matter in an
object (protons, neutrons, electrons)

Weight—the force that acts upon an
object from other things
Thought Question
On the Moon,
•   your weight is the same, your mass is less.

•   your weight is less, your mass is the same.

•   your weight is more, your mass is the same.

•   your weight is more, your mass is less.
Thought Question
On the Moon,
•   your weight is the same, your mass is less.

•   your weight is less, your mass is the same.

•   your weight is more, your mass is the same.

•   your weight is more, your mass is less.
Why are astronauts
weightless in space?
• There is no gravity in space.

• The force of gravity is much less.

• The moon is pulling astronauts in the other direction.

• The Earth’s magnetic field holds them up.

• They are massless.
Why are astronauts
weightless in space?

•   There is no gravity in space.
•   The force of gravity is much less.
•   The moon is pulling astronauts in the other direction.
•   The Earth’s magnetic field holds them up.
•   They are massless.
Why are astronauts
weightless in space?

•   There is no gravity in space.
•   The force of gravity is much less.
•   The moon is pulling astronauts in the other direction.
•   The Earth’s magnetic field holds them up.
•   They are massless.

Gravity IS pulling them towards Earth.
They ARE falling!
Why are astronauts
weightless in space?

• There is gravity in space.

• Weightlessness is due to a
constant state of free-fall.
How can they ORBIT?

• As spacecraft fall, they also move sideways

• At 300 miles above Earth:
•Falling towards Earth continuously, but…
•Moving at 17,000 miles per hour SIDEWAYS
•Fall “around” Earth!
Sir Isaac Newton

Invented the reflecting
telescope
Invented calculus
Connected gravity
and planetary forces
Philosophiae naturalis
principia mathematica
Universal Laws of Motion

“If I have seen farther than others, it
is because I have stood on the
shoulders of giants.”

Sir Isaac Newton (1642 – 1727)
Physicist
Newton’s Laws of Motion

1                         3

2
Newton’s 1st Law
A body at rest or in motion at a constant
speed along a straight line remains in that
state of rest or motion unless acted upon by
an outside force.

 Planets orbit stars stay in motion, but are
continually being pulled in their orbit by the star.

 Rockets heading to the moon or Mars, once
launched, can coast along a straight line.
Newton’s 2nd Law
The change in a body’s velocity due to an applied
force is in the same direction as the force and
proportional to it, but is inversely proportional to the
body’s mass.

F=ma
Launch a rocket – as fuel is used up, mass decreases,
and rocket accelerates even faster!
“Staging” rockets is even smarter!
Newton’s 3rd Law

For every applied force, a force of equal size but
opposite direction arises.

As rocket exhaust pushes backwards, the rocket itself
moves forwards
 As Earth pulls on the Moon, the Moon pulls on Earth
Universal Law of Gravitation
Between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the
distance between the centers of the objects.
Universal Law of Gravitation
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
Law of Gravity
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
Gravity is ONLY attractive!
There is no “anti-gravity”
Gravity
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.

What kind of Mass?
It doesn’t matter !
What shape, size, temperature, state?
It doesn’t matter!!
Illustrating Gravity with Tides

• Why are there two high tides each day?
• Why are tides on Earth caused primarily by
the Moon rather than by the Sun?
• Why is Earth’s rotation gradually slowing
down?
• Why does the Moon always show the same
face to Earth?
Tides

 Since gravitational force decreases with
(distance)2, the Moon’s pull on Earth is
strongest on the side closer to the Moon, and
weakest on the opposite side.
Tides

 Since gravitational force decreases with (distance)2, the
Moon’s pull on Earth is strongest on the side closer to
the Moon, and weakest on the opposite side.

 The Earth gets stretched along the Earth-Moon line.

 The oceans rise relative to land at these points.
Tides
 Every place on Earth passes through these
points, called high tides, twice per day as the
Earth rotates.

 High tides occur every 12 hours 25minutes
 remember, the Moon moves!

 The Sun’s tidal effect on Earth is not as strong.
 About ½ as large as the Moon
 But when BOTH stretch in the same direction,
even larger tides!
Tides
When Sun & Moon pull in the same
direction (new & full phases)

 high tide is HIGHER than usual
Tides

When Sun & Moon pull
at right angles
(first & last quarter
phases)

high tide is LOWER
than usual
Tidal Friction

 Reaction between Moon’s pull & Earth’s rotation.
 Earth’s rotation slows down (1 sec every 50,000 yrs.)
 Moon moves farther away from Earth.
Where’s the PROOF? Stromatolites!

Earth’s rotation slows down
Synchronous Rotation

 When rotation period of a moon, planet, or star
equals its orbital period about another object.

 Tidal friction on the Moon (caused by Earth)
has slowed its rotation down to 1 month.

 The Moon now rotates synchronously.
 We always see the same side of the Moon.
Orbital Paths

 Extending Kepler’s Law #1,
Newton found that ellipses
were not the only orbital paths.

 possible orbital paths
 ellipse (bound)
 parabola (unbound)
 hyperbola (unbound)
Newton’s Version of Kepler’s Third Law

Using calculus, Newton was able to derive
Kepler’s Third Law from his own Law of Gravity.
In its most general form:
2         2   3
P = 4 a / G (m1 + m2)
If you can measure the orbital period of two
objects (P) and the distance between them (a),
then you can calculate the sum of the masses
of both objects (m1 + m2).
Changing Orbits

orbital energy = kinetic energy +
gravitational potential energy

conservation of energy implies
orbits can’t change
spontaneously

An object can’t crash into a planet
unless its orbit takes it there.
Changing Orbits

An orbit can only change if it
gains/loses energy from
another object, such as a
gravitational encounter

If an object gains enough
energy so that its new orbit is
“unbound” it has reached
escape velocity.
Changing Orbits

We can use the gravitational
pull of planets to “slingshot”
spacecraft to other parts of
the solar system!

“Gravitational Assist” cuts travel
time to outer solar system by
years!

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